M, A, N and K stand in a row; based on the given information about their heights, which statements are sufficient to decide who stands last when arranged from shortest to tallest?

Introduction / Context:
This is a data sufficiency question about ordering by height. The goal is not to find exact heights but to check whether the given statements are enough to determine who will stand last when the four persons are arranged from shortest to tallest.

Given Data / Assumptions:

• Persons: M, A, N and K are standing in a row.
• Main question: If we arrange them from shortest to tallest, who is standing last?
• Statement 1: A is shorter than K.
• Statement 2: M is shorter than A.

Concept / Approach:
We need enough information to identify the tallest person uniquely. One or more inequality statements may give partial order, but unless every person's relative position is fixed, the data are insufficient. We test each statement alone and then both together to see whether N's position remains unspecified.

Step-by-Step Solution:
Step 1: From statement 1 alone, A is shorter than K, so K is taller than A. We know nothing about M or N relative to them. Step 2: From statement 2 alone, M is shorter than A, so A is taller than M. N's height is still unknown, and K's height is also unknown. Step 3: Combine both statements. We obtain M < A < K (M is shorter than A, A is shorter than K). K is taller than both M and A. Step 4: However, we still do not know where N stands. N could be shorter than M, between M and A, between A and K, or taller than K. Step 5: Because N's relative height is not fixed, we cannot decide who is tallest and hence who will stand last.

Verification / Alternative check:
Construct two scenarios. In scenario one, N is the tallest: let heights be M = 150 cm, A = 160 cm, K = 170 cm and N = 180 cm. In scenario two, K is the tallest: M = 150 cm, A = 160 cm, K = 180 cm and N = 165 cm. Both scenarios satisfy A < K and M < A, but the identity of the tallest person differs. This proves that the data do not fix a unique last person.

Why Other Options Are Wrong:
Option B claims that together the statements are sufficient, but our examples show otherwise. Options C and D incorrectly treat one statement alone as sufficient, which is clearly not the case since they say nothing about two of the persons. Option E also overstates sufficiency since neither statement alone answers the question.

Common Pitfalls:
A common mistake is to focus only on the three persons connected by the statements and ignore the fourth person whose position remains free. Always check whether every person's relative order is uniquely determined before calling the data sufficient.

Final Answer:
The correct evaluation is that statements 1 and 2 together are not sufficient to identify who will stand last.